During a financial panic, it is learned that Bank A has a 0.4 chance of collapsing in the next month and that, independently, Bank B has a 0.3 chance of failing. Bank C, which has heavy deposits in both A and B, has a 0.5 probability of failing if one of those banks collapses and a 0.7 chance if both of them fall apart. Otherwise, Bank C will stay afloat. (a) List the eight possible outcomes of the panic (with respect to the fates of the three banks). (b) Find the probability of each of the events identified in (a). What is the probability that all three banks survive the panic?
During a financial panic, it is learned that Bank A has a 0.4 chance of collapsing in the next month and that, independently, Bank B has a 0.3 chance of failing. Bank C, which has heavy deposits in both A and B, has a 0.5 probability of failing if one of those banks collapses and a 0.7 chance if both of them fall apart. Otherwise, Bank C will stay afloat. (a) List the eight possible outcomes of the panic (with respect to the fates of the three banks). (b) Find the probability of each of the events identified in (a). What is the probability that all three banks survive the panic?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Transcribed Image Text:During a financial panic, it is learned that Bank A has a 0.4 chance of collapsing in
the next month and that, independently, Bank B has a 0.3 chance of failing. Bank C,
which has heavy deposits in both A and B, has a 0.5 probability of failing if one of
those banks collapses and a 0.7 chance if both of them fall apart. Otherwise, Bank C
will stay afloat.
(a) List the eight possible outcomes of the panic (with respect to the fates of the
three banks).
(b) Find the probability of each of the events identified in (a).
What is the probability that all three banks survive the panic?
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